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Virgil
Posts:
9,012
Registered:
1/6/11


Re: WM's Matheology
Posted:
Jun 23, 2012 5:38 PM


In article <cf2c619e49a0499b9a709372cc209f18@cu1g2000vbb.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 23 Jun., 18:24, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > > WM <mueck...@rz.fhaugsburg.de> writes: > > > On 23 Jun., 15:50, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > > > > >> I've no idea what you're going on about now, but what makes a singleton > > >> a singleton is the fact that it contains only one element. > > > > > The real axis contains many irrational numbers. How can an irrational > > > number become a singleton? Why is there a number that is a singleton? > > > > This question makes no particular sense at all. > > That depends on your intelligence. Try harder. > > > Numbers do not become > > singletons[1]. > > That is blatantly wrong.
If one uses the standard meaning of "singleton" as being a set with exactly one member: http://en.wikipedia.org/wiki/Singleton_(mathematics) then numbers are NOT singletons (with the possible exception of the natural number 1, when it is defined as {{}} ).
But real numbers can be members of singletons, e.g., closed intervals of zero length.
The real numbers are not a completely > disconnected before all rationals are covered by intervals. After that > the uncovered real numbers a compkletely disconnected space, > consisting of singletons. So they have become singletons, no? No! To be precise, the maximal connected subsets of a completely disconnected space are singleton sets. By a common abuse of language, which should be avoided in the vicinity of WM, as he will always get muddled, one might casually refer to the member of the singleton as being the singleton. 



